We propose that the extraordinarily high superconducting transition temperatures in the cuprates are driven by an exact mapping of the d(x(2)-y(2)) Cooper-pair wavefunction onto the incommensurate spin fluctuations observed in neutron-scattering experiments. This is manifested in the direct correspondence between the inverse of the incommensurability factor δ seen in inelastic neutron-scattering experiments and the measured superconducting coherence length ξ(0). Strikingly, the relationship between ξ(0) and δ is valid for both La(2-x)Sr(x)CuO(4) and YBa(2)Cu(3)O(7-x), suggesting a common mechanism for superconductivity across the entire hole-doped cuprate family. Using data from recent quantum-oscillation experiments in the cuprates, we propose that the fluctuations responsible for superconductivity are driven by a Fermi-surface instability. On the basis of these findings, one can specify the optimal characteristics of a solid that will exhibit 'high T(c)' superconductivity.